Equilibrium constant Haldane relations

For reversible enzymatic reactions, the Haldane relationship relates the equilibrium constant KeqsNith the kinetic parameters of a reaction. The equilibrium constant Keq for the reversible Michaelis Menten scheme shown above is given as... 

The importance of the Haldane relationship Eq. (42) relates to the fact that the kinetic parameters of a reversible enzymatic reaction are not independent but are constraint by the equilibrium constant of the overall reaction [157]. 

Applying the Haldane relation to obtain an equilibrium constant from initial rate kinetics. Because of the inherently greater uncertainty in determinations of rate parameters, this method often proves to be unreliable ... 

A mathematical equation indicating how the equilibrium constant of an enzyme-catalyzed reaction (or half-reaction in the case of so-called ping pong reaction mechanisms) is related to the various kinetic parameters for the reaction mechanism. In the Briggs-Haldane steady-state treatment of a Uni Uni reaction mechanism, the Haldane relation can be written as follows ... 

Fromm and Cleland provide valuable discussions of the utility of Haldane relations in excluding certain kinetic reaction mechanisms based on a numerical evaluation of the constants on each side of the equal sign in the Haldane relation. If the equality is maintained, the candidate mechanism is consistent with the observed rate parameter data. Obviously, one must be concerned about the quality of experimentally derived estimates of rate parameters, because chemists have frequently observed that thermodynamic data (such as equilibrium constants) are often more accurate and precise than kinetically derived parameters. See Haldane Relations for Multisubstrate Enzymes... 

The Haldane equation does not relate the equilibrium constant between ES and EP to that between S and P in solution. The equilibrium constant for the enzyme-bound reagents is often very different from that in solution for several reasons ... 

Aminoacyl adenylates have long been known to be high energy compounds, but their free energies of hydrolysis had not been accurately measured. This was accomplished for tyrosyl adenylate using the Haldane approach (Chapter 3, section H) and mutants of the tyrosyl-tRNA synthetase. The equilibrium constant for the formation of tyrosyl adenylate in solution (Absolution) = [Tyr-AMP] [PPi]/ [Tyr] [ATP]) is related to the rate and equilibrium constants for the enzymatic reaction illustrated in Figure 15.21 by equation 15.8. 

A Haldane equation can be formulated by setting the numerator to zero, resulting in a relation for the equilibrium constant (Eq. (43)) ... 

The equilibrium constant of the overall catalyzed reaction is related to kinetic coefficients for the forward and reverse reactions by the Haldane relation (5,6)... 

This equation now expresses initial net forward rate for the conversion of substrate into product in the presence ofsignificant concentrations ofboth [S] and [P]. Any relationship that relates any equilibrium constant to kinetic rate constants is known as a Haldane relationship. Equation (8.61) is a typical Haldane relationship. Therefore, the operation using Equation (8.61) to simplify Equation (8.60) to give (8.62) is known as a Haldane simplification -owing to the use of a Haldane relationship to effect the simplification. Clearly, if there is no... 

The various kinetic constants for any bisubstrate or trisubstrate steady-state mechanism are related to the thermodynamic equilibrium constant by Haldane equations of the general type ... 

The Haldane Relationship. Another of the properties of enzyme systems frequently measured is the equilibrium constant of the over-all reaction. This is the means for determining a fundamental thermodynamic property, the free enei (F) of a reaction. Free energy will be discussed later. At this point a relation between enz3uue kinetics and equilibrium is of interest. The equilibrium constant for a reaction... 

There can be many reasons why a reaction does not proceed to equilibrium. The standard free energy, then, does not define the amount of work that will be obtained from a reaction it is the maximum energy available under defined conditions. When the standard free energy is known, it can be used to determine the equilibrium constant of a reaction. This, it must be remembered, measures the extent to which a reaction may proceed, but it does not indicate the speed of a reaction or even that a reaction will occur at all. AF is related indirectly to the relative rates of enzyme-catalyzed reactions by the Haldane relationship (p. 12), but the absolute rate of reaction is determined by the amount of enzyme and substrate in a given system. 

For the sequence of processes (5.8) the equilibrium constant, related to the reagents in aqueous solution, can be expressed using the Haldane relationship... 

Equations (3.3.27) and (3.3.28) are referred to as the Haldane relations in recognition of the original derivation by Haldane (1930). It can readily be shown that the overall equilibrium constant of a consecutive reaction is the... 

This is exactly what the Haldane relations demonstrate for the sequence of intermediates in enzyme reactions. They are useful criteria when changing Michaelis parameters are compared to the equilibrium constant for an enzyme catalysed reaction. We shall return to this problem in section 5.1, when we discuss how transient kinetic analysis can be used to determine the equilibrium constants of individual steps. In this connection the equations which express the concentrations of the intermediates in terms of the fraction of total amount of enzyme in the reaction mixture will turn out to be useful. Many enzyme reactions can be studied in both directions and the two sets of parameters for the reactions starting on either side (with S or P as the substrate) - Kh, and - give further insight. 

In chapter S the phenomenon of on enzyme equilibria is discussed with examples. This refers to the fact that the equilibrium between enzyme-substrate and enzyme-product complexes is often near unity, even if the overall equilibrium constant for the interconversion of free substrate to free product is a large number. This does not contradict the statement that enzymes (or catalysts in general) do not affect equilibrium constants of reactions. It has to be remembered that this definition of catalysis only applies to the equilibrium between free substrates and products. An example, which illustrates this in terms of the Haldane relation, is heart lactate dehydrogenase. By the methods discussed in section 5.1 it was shown that the equilibrium constant for the two complexes... 

In modeling of enzymatic reactions, a Haldane relationship relating the kinetic parameters to the equilibrium constant for that reaction is often used. Similar approaches are applied in heterogeneous and homogeneous catalysis. 

This relation, representing the ratio of the rate constants of the first order kinetics is known as the Haldane equation . Haldane equations can be formulated for every kinetic model describing an equilibrium reaction, just by setting the numerator to zero. 

The initial rate equation derived by steady-state analysis is of the second degree in A and B (SO). It simplifies to the form of Eq. (1) if the rates of dissociation of substrates and products from the complexes are assumed to be fast compared with the rates of interconversion of the ternary complexes k, k )] thus, the steady-state concentrations of the complexes approximate to their equilibrium concentrations, as was first shown by Haldane (14)- The kinetic coefficients for this rapid equilibrium random mechanism (Table I), together with the thermodynamic relations KeaKeab — KebKeba and KepKepq — KeqKeqp, suffice for the calculation of k, k and all the dissociation constants Kea = k-i/ki, Keab = k-i/ki, etc. 

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